Yes.
You capitalize the "s" for state when you referring to a specific state or state agency; State of Texas or State of Maine or The State Dept. of Health. You don't capitalize the "s" when the word state is used in general terms; the states with the largest population or the western most state.
It is capitalized Western Europe
If thename of the waltz is Wester n, the n it is capitalized. It should be Wester n Waltz.
When the w is capitalized.
The term "southern states" should only be capitalized if it is used as part of a proper noun referring to a specific group of states, such as the Southern States of the United States. Otherwise, it should be written in lowercase.
Yes, you should capitalize "About" in a title.
You should capitalize "American" when referring to the nationality or citizenship of someone from the United States, as in "American citizen." However, you do not capitalize it when referring to general concepts or things relating to America, such as "the American culture."
You should capitalize "State" when it is used as part of the official name, so it is "State of Minnesota." This is similar to how you would capitalize "United States" or "Commonwealth of Massachusetts." However, when referring to the state in a general sense, you would use "state of Minnesota."
Yes, you should capitalize 'President' when it refers to a specific person ('The President of the United States'). It should be left uncapitalized when it is non-specific (Past presidents have included ... ').
Doesn't need to be, but you see it both ways, as well as Western hemisphere.
Yes, you should capitalize the C in Century.
'US' must be captialized, but for the 'the' you should only capitalize it if it is at the start of a sentence (Eg: The US is a big country).